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February 29, 2024
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# Fractions: An In-Depth Look

When thinking of fractions, many people think of the type they see on a pie chart or some other circular bar graph. For example, there may be three pieces of pie, each with one-third (1/3) of the pie. The bottom number (the denominator) is how many equal parts of whatever is being measured are in that fraction; for this example, the pie would have three equal parts. The top number (the numerator) tells you what part you can find out of those total parts; in this case, 1 out of 3 equals 1/3.

However, there are more types than just these fractions used in day-to-day life. There are also mixed numbers and decimals which will be explained here. A decimal is similar to a fraction in that there is an integer (the bottom number) and another part (the top number). With fractions, one of the integers is always 1, while with decimals it is usually “1.” However, they can have more than one digit after the decimal point and fraction to decimal which will be shown in this article

First off, mixed numbers are what they sound like- a combination of both an integer and a fraction. They look something like this: 2 3/4. It means two whole numbers added together with three fourths or just looking at it another way round two thirds plus one fourth. A mixed number looks complicated but actually, isn’t that hard if one approaches it a certain way.

Remember that a fraction is a number over another number, so two-thirds would be shown as 2/3. So if one adds them together, the result will be (2 + 2)/3, or in other words 4/3. If you add an integer to a fraction it will still make sense because of this- fractions can be expressed any number of times on top of one whole but they can never go below zero. Therefore if an integer is added to a fraction the result will always be above zero and therefore still make sense. For example: 1 1/2 + 3 = 3 1/2

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### To convert fraction to decimal, Subtract the denominator from the numerator.

Now comes the fun part – dividing fractions! Dividing one fraction by another usually looks something like this: 2/8

Consider a pizza cut into eight pieces with one piece being first on the left and the eighth being first on the right. It is similar to what you would see if dividing two fractions from opposite ends of the whole number line where one denominator is larger than another but both numerators are smaller. To divide these fractions, start at 0 as usual and count how many spaces over from 0 each fraction would sit (one-eighth would be 8 spaces over). To make sure they get the same result every time, always divide by the smallest denominator (in this case 2) first. So to divide the fractions and get the same result every time, one simply needs to count 8 spaces over from 0 and mark that spot. Then count two additional spaces over and mark that space as well.

In this case, one-eighth would be divided by 2 first because it is smaller than 3/4 which is what three-fourths would be divided by. One-eighth divided by 2 is 1/4. Three-fourths divided by 2 is 3/8. The final fraction would be 4/8 because of the same reason as before: adding an integer to a fraction will always make a result above zero which makes sense with a product of fractions being below the whole number line where anything multiplied by zero will be zero.

So if one knows the fractional values of each division, all they need to do is add them together and get the fraction you started with. That is why dividing fractions is quite easy.

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